To address this problem, [1]} proposed an alternative frequentist \(L^2\)  calibration approach. In this case, let \(\theta _{L^2}\)  denote the values of the calibration parameters that minimise the squared norm (in the associated \(L^2\)  space) of the bias function. Correspondingly, [1]} defined an estimator given by the values of the calibration parameters that minimise a loss function given by the \(L^2\)  norm of the difference between a non-parametric estimator of \(\mu (\mathbf {x})\)  and the mathematical model \(\eta (\mathbf {x}, \theta )\) . [1]} showed that this estimator is consistent for \(\theta _{L^2}\) . Alternatively, [4]} showed that the ordinary least squares estimator of the calibration parameters is also consistent for \(\theta _{L^2}\) . Furthermore, for uncertainty quantification, [4]} proposed a bootstrapping procedure to provide confidence intervals for the calibration parameters.
